Related papers: BV quantization of the Rozansky-Witten model
We describe a globalization construction for the Rozansky-Witten model in the BV-BFV formalism for a source manifold with and without boundary in the classical and quantum case. After having introduced the necessary background, we define an…
The present work contains a complete formulation of the Batalin-Vilkovisky (BV) formalism in the framework of locally covariant field theory. In the first part of the thesis the classical theory is investigated with a particular focus on…
This paper is mainly based on the talk I presented at the meeting "The Philosophy and Physics of Noether's Theorems" that took place 5-6 October 2018, but it also contains some original results that were inspired by discussions with…
Into a geometric setting, we import the physical interpretation of index theorems via semi-classical analysis in topological quantum field theory. We develop a direct relationship between Fedosov's deformation quantization of a symplectic…
This is a survey of our program of perturbative quantization of gauge theories on manifolds with boundary compatible with cutting/pasting and with gauge symmetry treated by means of a cohomological resolution (Batalin-Vilkovisky) formalism.…
We investigate the generic 3D topological field theory within AKSZ-BV framework. We use the Batalin-Vilkovisky (BV) formalism to construct explicitly cocycles of the Lie algebra of formal Hamiltonian vector fields and we argue that the…
We show that the local observables of the curved beta gamma system encode the sheaf of chiral differential operators using the machinery of the book "Factorization algebras in quantum field theory", by Kevin Costello and the second author,…
As a detailed application of the BV-BFV formalism for the quantization of field theories on manifolds with boundary, this note describes a quantization of the relational symplectic groupoid for a constant Poisson structure. The presence of…
We report a rigorous quantization of topological quantum mechanics on $\mathbb{R}_{\geqslant 0}$ and $\mathbf{I}= [0, 1]$ in perturbative BV-BFV formalism. Costello's homotopic renormalization is extended, and incorporated in our…
We construct a formal global quantization of the Poisson Sigma Model in the BV-BFV formalism using the perturbative quantization of AKSZ theories on manifolds with boundary and analyze the properties of the boundary BFV operator. Moreover,…
We apply the modern Batalin-Vilkovisky quantization techniques of Costello and Gwilliam to noncommutative field theories in the finite-dimensional case of fuzzy spaces. We further develop a generalization of this framework to theories that…
We investigate various aspects of invariance under local symmetries in the framework of perturbative algebraic quantum field theory (pAQFT). Our main result is the proof that the quantum Batalin-Vilkovisky (BV) operator, on-shell, can be…
We show that the classical Batalin--Vilkovisky cohomology at negative ghost number of the spinning particle, observed in ref. arXiv:1511.02135, is removed by a Koszul--Tate resolution involving saturation of Grassmann odd variables. The…
We provide a formulation of quantum mechanics based on the cohomology of the Batalin-Vilkovisky (BV) algebra. Focusing on quantum-mechanical systems without gauge symmetry we introduce a homotopy retract from the chain complex of the…
In this paper, we study the third quantized super-group field cosmology, a model in multiverse scenario, in Batalin-Vilkovisky (BV) formulation. Further, we propose the superfield/super-antifield dependent BRST symmetry transformations.…
We review the Lagrangian Batalin--Vilkovisky method for gauge theories. This includes gauge fixing, quantisation and regularisation. We emphasize the role of cohomology of the antibracket operation. Our main example is $d=2$ gravity, for…
The general procedure for obtaining explicit expressions for all cohomologies of N.Berkovits's operator is suggested. It is demonstrated that calculation of BV integral for the classical Chern-Simons-like theory (Witten's OSFT-like theory)…
We study linear Batalin-Vilkovisky (BV) quantization, which is a derived and shifted version of the Weyl quantization of symplectic vector spaces. Using a variety of homotopical machinery, we implement this construction as a symmetric…
In this Letter we consider the perturbative quantum gravity on the super-manifold which remains invariant under absolutely anticommuting BRST and anti-BRST transformations. In addition to that the theory posses one more symmetry known as…
We address the treatment of gauge theories within the framework that is formed from combining the machinery of noncommutative symplectic geometry, as introduced by Kontsevich, with Costello's approach to effective gauge field theories…